Final answer:
The greatest common factor (GCF) of the numbers 12, 28, and 24 is found by identifying the smallest powers of their common prime factors, which are 2 and 3. Multiplying these together, 2 squared times 3, gives us the GCF of 12.
Explanation:
To find the greatest common factor (GCF) of the numbers 12, 28, and 24, we break each number down into its prime factors:
28 = 2 x 2 x 7
The smallest power of 3 that is common is just 3.
Therefore, the GCF of 12, 28 and 24 is 22 x 3 = 4 x 3 = 12.
SOMEBODY HELP ME WITH THESE PLEASE! I really need the help like NOW PLS!
Answer:
97.
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).
99.
Step-by-step explanation:
The transformation from f to g represents a __________ stretch. f(x) = Square root of x. and g(x) = 6Square root of x.
The transformation from f to g represents a Vertical stretch.
Step-by-step explanation:We are given a parent function f(x) as:
[tex]f(x)=\sqrt{x}[/tex]
and the transformed function g(x) as:
[tex]g(x)=6\sqrt{x}[/tex]
We know that any function transformation of the type:
f(x) → a f(x)
represents either a vertical stretch stretch or compression depending on the value of a.
If 0<a<1 then the transformation is a vertical compression and if a>1 then the transformation is a vertical stretch.
Here we have a=6>1
Hence, the transformation is a VERTICAL STRETCH.
Solve the equation ,and check the solution.
r - 3 r
____ = __
10 13 Check:
To solve the equation, we cross multiply to eliminate the fractions and solve for r. The solution is r = 13. We can check the solution by substituting it back into the original equation.
Explanation:To solve the equation (r - 3) / 10 = r / 13, we can cross multiply to eliminate the fractions. This gives us 13(r - 3) = 10r. Distributing, we get 13r - 39 = 10r. We can then solve for r by subtracting 10r from both sides and adding 39 to both sides. This gives us 3r = 39. Dividing both sides by 3, we find that r = 13.
To check the solution, we substitute r = 13 back into the original equation. The left side becomes (13 - 3) / 10 = 10 / 10 = 1, and the right side becomes 13 / 13 = 1. Since both sides are equal to 1, we can confirm that the solution r = 13 is correct.
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Line BC has an equation of a line y = 2x + 3, and line EF has an equation of a line y = negative one over 2 x + 4. These two equations represent
Answer:
Perpendicular lines.
Step-by-step explanation:
We have been given that line BC has an equation of a line [tex]y=2x+3[/tex] and line EF has an equation of a line [tex]y=-\frac{1}{2}x+4[/tex]. We are asked to determine what these both equations represent.
We know that slope of two perpendicular lines is negative reciprocal of each other. This means the product of slope of both lines is equal to [tex]-1[/tex].
Let us find the product of slopes of both lines.
[tex]2\times \frac{-1}{2}[/tex]
Upon cancelling 2 with 2 we will get,
[tex]=-1[/tex]
Therefore, the given two equations represent equations of two perpendicular lines.
A rectangular garden has length twice as great as its width. A second rectangular garden has the same width as the first garden and length that is 4 meters greater than the length of the first garden. The second garden has area of 70 square meters. What is the width of the two gardens?
A basket contains 11 pieces of fruit: 4 apples, 5 oranges, and 2 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?
The probability that Jonas will get an orange and Beth will get an apple is 20/121.
Explanation:To find the probability that Jonas will get an orange and Beth will get an apple, we need to find the probability of Jonas getting an orange and then multiply it by the probability of Beth getting an apple.
The probability of Jonas getting an orange is the number of oranges in the basket (5) divided by the total number of fruits (11):
P(orange for Jonas) = 5/11
The probability of Beth getting an apple is the number of apples in the basket (4) divided by the total number of fruits (11):
P(apple for Beth) = 4/11
To find the combined probability, we multiply these two probabilities together:
P(orange and apple) = P(orange for Jonas) * P(apple for Beth) = (5/11) * (4/11) = 20/121
Write an equation for the line that is parallel to the given line and that passes through the given point.
y = 1/2 – 8; (–6, –17)
A.) y = 2x – 14
B.) y = 1/5x + 5/2
C.) y = -2x + 14
D.) y = 1/2x – 14
How to go from sum of products to product of sums?
Multiplication gives us distribution over the products, so
(a′+b+d′) (a′+b+c′+f′) = a′ (a′+b+c′+f′) + b (a′+b+c′+f′) + d′ (a′+b+c′+f′)
And then you can then distribute again each of the factors on the right.
Then you should simplify in any given number of ways. To take as an example, you have a′b and ba′, and since a′b + a′b = a′b + a′b = a′b, you can just drop one of them. Since bb = b, you can rewrite bb as b and etc.
So in the end part we should arrive at a sum of products. Then you can just invert. For example, if at the end you had:
p′ = a′b + bc′ + d′f ′+ a′f′
Then we would have
p = p′′ = (a′b + bc′ + d′f′ + a′f′)′ = (a′b)′⋅(bc′)′⋅(d′f′)′⋅(a′f′)′
Then applying De Morgan's laws to each of the factors, e.g., (a′b)′ = a+b′, so we would have
p = (a+b′)⋅(b′+c)⋅(d+f)⋅(a+f)
which is a product of sums.
If measure of angle p=(10x-2),measure of angle o=(3x+9) , and measure of angle q=(3x-3) , list the lengths of the sides of triangle OPQ from longest to shortest.
Answer:
OQ > PQ > OP
Step-by-step explanation:
In this question measure of all angles in a triangle has been given.
m∠ p = (10x - 2)
m∠ q = (3x - 3)
m∠ o = (3x + 9)
Since total of all angles is 180°, so we will equate the total of all angles to 180°
∠p + ∠q + ∠o = 180°
(10x - 2) + (3x - 3) + (3x + 9) = 180°
(10x + 3x + 3x) -2 - 3 + 9 = 180
16x - (2 + 3 - 9) = 180°
16x + 4 = 180
16x = 180 - 4
16x = 176
x = [tex]\frac{176}{16}=11[/tex]
Now we will find the measure of each angle.
∠p = (10x - 2) = 10×11 - 2 = (110 - 2) = 108°
∠q = (3x - 3) = 3×11 - 3 = (33 - 3) = 30°
∠o = (3x + 9) = 3×11 + 9 = (33 + 9) = 42°
As we know in a triangle, angle opposite to the largest side is largest and angle opposite side is the smallest.
Since ∠p > ∠o > ∠q
Therefore, in Δ OPQ opposite sides to these angles will be in the same ratio.
OQ > PQ > OP
Evaluate S5 for 400 + 200 + 100 + … and select the correct answer below.
25
775
1,125
500
The sum of first five terms for the geometric series is 775. The correct answer is (B).
What is a geometric sequence?In a geometric sequence, the ratio of two consecutive terms are always equal.
The general expression for the nth term is given as aₙ = a₁ × rⁿ⁻¹ .
The sum of n terms for this sequence is given as Sₙ = (rⁿ - 1)/(r - 1)
The given series is 400 + 200 + 100 + …
It is a geometric series.
Its first term is a₁ = 400.
And, common ratio is r = 200/400 = 0.5.
Now, the expression for the sum of n terms is given as below,
Sₙ = a(1 - rⁿ)/(1 - r)
Then, substitute the value of a₁, a₅ and n = 5 to obtain,
S₅ = 400(1 - 0.5⁵)/(1 - 0.5)
⇒ S₅ = 775.
Hence, the sum of first five terms of the given series is 775.
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A rectangular prism with a square base has a lateral area of 192 square yards and a surface area of 264 square yards. What is the length of a base edge?
traveling at 65 miles per hour how many minutes rounded to the nearest whole number does it takes to drive 125 miles from san digit to malibu
divide total miles by speed
125/65 = 1.923 hours
there are 60 minutes per hour
multiply 1.923*60 = 115.384 minutes
rounded off to nearest whole number = 115 minutes
Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.
Part A: Find (f + g)(x). Show your work. (3 points)
Part B: Find (f ⋅ g)(x). Show your work. (3 points)
Part C: Find f[g(x)]. Show your work. (4 points)
What is the value of the fourth term in a geometric sequence for which a1 = 30 and r = 1/2?
The value of the fourth term in the geometric sequence is 3.75.
Explanation:The value of the fourth term in a geometric sequence can be found using the formula:
an = a1 * r(n-1)
Given that a1 = 30 and r = 1/2, we can substitute these values into the formula and solve for a4:
a4 = 30 * (1/2)(4-1) = 30 * (1/2)3 = 30 * (1/8) = 3.75
Therefore, the value of the fourth term in the geometric sequence is 3.75.
Final answer:
The value of the fourth term in the geometric sequence is 3.75.
Explanation:
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio. In this case, the first term (a1) is 30 and the common ratio (r) is 1/2. To find the fourth term, we can use the formula:
an = a1 * r(n-1)
Substituting the values given, we have:
a4 = 30 * (1/2)(4-1)
Simplifying this expression, we get:
a4 = 30 * (1/8) = 3.75
Therefore, the value of the fourth term in this geometric sequence is 3.75.
(Solve for r) 0.5r − 3.8 = 5.66
I don't get it I got a different answer then these
Find the total area of the prism in ( _+_√_ )
A rectangle is 42 square feet. what percent of the area of the rectangle is a square with side lengths of 6 feet?
area = L x w
42 = 6 x w
w=42/6 = 7
rectangle is 6 x 7
square would be 6 x 6 = 36 square feet
36/42 = 0.857 = 85.7% ( Round answer if needed)
(25 Points)Enter numbers to write 4.23×10^3 in standard notation.
A pizza delivery shop averages 20 minutes per delivery with a standard deviation of 4 minutes. What is the probability that a pizza takes less than 15 minutes to be delivered?
A) side-side-side triangle similarity postulate
B) angle-angle triangle similarity postulate
C) angle-side-angle triangle similarity postulate
D) hypotenuse-lag triangle similarity postulate
What is the length of a diagonal of a cube with a side length of 10 cm? 200cm, 210cm, 300cm, 320cm
The solution is, 10√3cm is the length of a diagonal of a cube with a side length of 10 cm.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
given that,
the side length is 10cm ,
then the length of diagonal of the base of the cube(x) is
X² =(10)²+(10)²
=200cm
so x = 10√2cm
so the length of diagonal of the cube(y) is
y² = (10)² + (10√2)²
=300
so y =10√3cm
Hence, The solution is, 10√3cm is the length of a diagonal of a cube with a side length of 10 cm.
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1. is acute. 2. is isosceles. 3. is right. Which two statements contradict each other?
Answer:
the answer is 2 and 3
Step-by-step explanation:
I took the test
let n be the first 3 of consecutive even integers. what is the sum of those integers?
(07.05 MC)
An equation is shown below:
4x + 2(x – 3) = 4x + 2x – 11
Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)
Part B: Name one property you used to solve this equation. (4 points
Answer:
-6 = -11
Distributive Property
Step-by-step explanation:
A.
4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 4x + 2x - 11
6x - 6 = 6x - 11
-6 = -11
since -6 is not equal to -11, so there's no solution
B. Distributive property
What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y=1/2x+4?
(02.02 MC)
Line segment RS is shown on a coordinate grid:
The line segment is rotated 270 degrees counterclockwise about the origin to form R'S'. Which statement describes R'S'?
R'S' is parallel to RS.
R'S' is half the length of RS
. R'S' is twice the length of RS.
R'S' is equal in length to RS.
The sum of four consecutive whole numbers is 54, what are the four numbers
The length of LN is 28 centimeters. What is the length of LP?
Answer:
we need a diagram or somthing
Step-by-step explanation:
What are the roots of the function y = 4x2 + 2x – 30? To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of .
Next, factor the trinomial completely. The equation becomes .
Use the zero product property and set each factor equal to zero and solve. The roots of the function are .
The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2
Roots of a quadratic equationThe given quadratic equation is:
[tex]y=4x^2+2x-30[/tex]
Set y = 0
[tex]4x^2+2x-30=0[/tex]
Factor the trinomial completely
[tex]4x^2-10x+12x-30=0\\\\2x(2x-5)+6(2x-5)=0\\\\(2x-5)(2x+6)=0[/tex]
Set each factor to zero and solve
2x - 5 = 0
2x = 5
x = 5/2
2x + 6 = 0
2x = -6
x = -6/2
x = -3
The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2
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